Breaking mirror symmetry

Weissbuch I, Leiserowitz L, Lahav M (2005) Stochastic Mirror Symmetry Breaking via Self-Assembly, Reactivity and Amplification of Chirality Relevance to Abiotic Conditions. 259 123-165... 

Crystallization and reactivity in two-dimensional (2D) and 3D crystals provide a simple route for mirror-symmetry breaking. Of particular importance are the processes of the self assembly of non-chiral molecules or a racemate that undergo fast racemization prior to crystallization, into a single crystal or small number of enantiomorphous crystals of the same handedness. Such spontaneous asymmetric transformation processes are particularly efficient in systems where the nucleation of the crystals is a slow event in comparison to the sequential step of crystal growth (Havinga, 1954 Penzien and Schmidt, 1969 Kirstein et al, 2000 Ribo et al 2001 Lauceri et al, 2002 De Feyter et al, 2001). The chiral crystals of quartz, which are composed from non-chiral Si02 molecules is an exemplary system that displays such phenomenon. 

Strong Chiral Amplification, Extreme Sensitivity and Mirror-Symmetry Breaking... 

The results of Soai and coworkers [35] as well as those of Singleton and Vo [36] suggest the occurrence of mirror-symmetry breaking in the Soai reaction, which is a rare phenomenon that is basically limited to a few crystallization processes [37]. Under certain kinetic conditions, chiral autocatalysis... 

Fluctuations are inherent to any experimental chemical system. Even if these fluctuations are infinitesimally small, they are sufficient to drive the system away from an unstable state. The optically active state is characterized by two equivalent options starting from an unstable racemic situation, the system can evolve into either an R configuration or into an S one. However, each individual experiment remains unpredictable as to which of the optically active states the system will move towards. For a large number of experiments an equal and random distribution between R and S dominance is expected if the initial conditions do not involve any preferences. Due to this unpredictability of the chiral configuration, the phenomenon of mirror-symmetry breaking introduces another element of stochastic behavior into chemical reactions different from that occurring in clock reactions [38,39]. 

Besides the effect of strong chiral amplification in the Soai reaction there is the experimental observation of spontaneous generation of ee from entirely achiral starting conditions. Fig. 4 shows that the kinetic model can give rise to mirror-symmetry breaking. 

For Fig. 4, the rate constant for the mutual inhibition (fo) was chosen as the bifurcation parameter however, all other parameters and the initial reactant concentrations serve as bifurcation parameters as well. Mirror-symmetry breaking in simulation is caused by the intrinsic instability of the autocat-alytic model. When placed into the proper parameter domain, this instability can be revealed by the inevitable machine round-off as well as by slightly... 

Fig. 4 Numerical simulation revealing mirror-symmetry breaking in which k.2 acts as a bifurcation parameter (same conditions as in Fig. 3 except [R]o + [S]o = 0). Each dot represents the final ee of an individual computer simulation. For k2 > 6 x 103 M-1 s-1 the system becomes optically active, where positive and negative values of the resulting ee are equally distributed...

The simulation shown in Fig. 6 demonstrates that a close to 1 1 ratio of homo- and heterochiral species can be reproduced, even under conditions in which the thermodynamic stability of the heterochiral dimers is considered higher than that of the homo chiral ones. This effect results from the nonlinear dynamics of the reaction and from mirror-symmetry breaking. 

A closer exploration of the parameter space showed that symmetry breaking is sensitive to the thermodynamic stabilities of the dimers but also to the rate of their formation, predicting that the heterochiral dimers are formed faster and are more stable than the homochiral ones [69]. The fitting of the experimentally obtained data (Fig. 5) resulted in rate parameters that confirm these conclusions and that simultaneously give rise to mirror-symmetry breaking. 

We have given kinetic insight into a number of experimental features of the Soai reaction. It was shown that chiral amplification and mirror-symmetry breaking are driven by a reaction network that contains enantioselective autocatalysis and mutual inhibition as the essential ingredients. In this sense, the Soai reaction moves the early concepts of Frank forward into experimental reality. Taking into account the formation of isopropylzinc alkoxide dimers, an evaluation of the parameter space in which amplification and symmetrybreaking are observed indicates that the heterochiral dimers display a higher thermodynamic stability and have to be formed faster than the homochiral ones. The necessity of such sensitive interplay may explain why such reactions systems are so scarce. 

Stochastic "Mirror Symmetry Breaking" via Self-Assembly, Reactivity and Amplification of Chirality ... 

Stochastic Mirror Symmetry Breaking by Spontaneous Self-Assembly. . 126... 

Soai s Auto-Catalytic System for Spontaneous Mirror Symmetry Breaking. 145... 

Chiral surfaces Enantiomorphous crystals Homochiral peptides Mirror symmetry breaking Non-linear kinetics Self-replication of peptides... 

The occurrence of reduction of symmetry is of particular importance in the mirror symmetry breaking process of racemic a-amino acids, accomplished with the assistance of crystals of glycine grown at interfaces. When grown from aqueous solutions, glycine crystallizes in its centrosymmetric a-polymorph (space group P2 /n). This crystal is composed from chiral... 

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